Abstract
A detailed derivation is given of a quantitative theory of vibrational relaxation in solids, that is a generalized version of a recent model for these processes. Formal analysis and numerical calculations with this model yield the following results: (1) Legay's empirical correlation between the relaxation rate and the impurity rotational constant is derived systematically, as an approximation for the model. (2) The range of molecular parameters is quantitatively established for which a transition takes place from a multiphonon relaxation mechanism to a multiroton one. (3) Quantitative estimates are made on the effect of various geometric distortions on the process: displacement from fee to hcp structure; vacancy at nearest neighbour site; impurity—nearest neighbour distance shrinking (due to chemical complex formation). The first type of distortion is found to have a negligible effect, but the third type enhances the rate by a factor of 10–10 3. (4) Impurity mass asymmetry has an extremely large effect on the rate when the rela experimental findings. New experiments are suggested to test predictions of the theory.
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